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Exciton longitudinal

Bulk silicon is a semiconductor with an indirect band structure, as schematically shown in Fig. 7.12 c. The top of the VB is located at the center of the Brillouin zone, while the CB has six minima at the equivalent (100) directions. The only allowed optical transition is a vertical transition of a photon with a subsequent electron-phonon scattering process which is needed to conserve the crystal momentum, as indicated by arrows in Fig. 7.12 c. The relevant phonon modes include transverse optical phonons (TO 56 meV), longitudinal optical phonons (LO 53.5 meV) and transverse acoustic phonons (TA 18.7 meV). At very low temperature a splitting (2.5 meV) of the main free exciton line in TO and LO replicas can be observed [Kol5]. [Pg.138]

Nevertheless, certain collective excitations can occur in the condensed phase. These may be brought about by longitudinal coulombic interaction (plasmons in thin films) or by transverse interaction, as in the 7-eV excitation in condensed benzene, which is believed to be an exciton [12]. Special conditions must be satisfied by the real and imaginary parts of the dielectric function of the condensed phase for collective excitations to occur. After analyzing these factors, it has been concluded that in most ordinary liquids such as water, collective excitations would not result by interaction of fast charged particles [13,14]. [Pg.11]

Typical luminescence spectra of as-grown crystals show ultra-violet emission due to free excitons (including their longitudinal optical phonons-EO replicas) as well as t5 ical bands of green and yellow-orange luminescence (the temperature is 77-80 K). When the temperature is 4.2 K, the luminescence of bound excitons (including their LO - replicas) dominates. ... [Pg.70]

In the present report, three subjects are to be reviewed (i) The triplet structure of excitons and the upper valence band (ii) the full set of the fundamental optical functions in the 0-30 eV energy range for polarizations E II c, E J. c, and their theoretical analysis and (iii) the main parameters of the elementary transverse and longitudinal transition components in the 0-30 eV energy range for polarizations E c, E L c, and their theoretical analysis. [Pg.172]

The analysis of the S2 and -Ims" spectra allowed to determine the energy values of transverse and longitudinal exciton transitions, and to evaluate their band areas and oscillator strengths (Tab. 1) the values off, given here, have been enlarged 10. ... [Pg.174]

For the first time, the full sets of exciton optical fundamental functions of ZnO have been calculated at 1.6, 4.2, and 90 K. The most correct energy values of transverse and longitudinal exciton transitions of the three series, together with their areas and oscillator strengths, have been determined, as well as their characteristic features. [Pg.180]

The long-wavelength field can be easily found if we take into account that in a medium without external charges the longitudinal component of the induction vector T> vanishes, and the macroscopic electric field is longitudinal, if the retardation, as assumed in the theory of Coulomb excitons, is not taken into account. From this considerations we obtain... [Pg.18]

For the longitudinal excitons, p = py and T(j,k,/x) = 0 as follows from (4.11). In consequence, those excitons do not interact with the transverse photons and retardation effects for them are not essential. From (4.17) and (4.18) we obtain for the longitudinal excitons35... [Pg.110]

The crystal possesses cubic symmetry. In this case exciton states, which correspond to nonvanishing values f1M(s), are either longitudinal exciton states (p = p,, P (k, p, ) s), or transverse exciton states, which for k —> 0 corresponds to the two-fold degenerate exciton band... [Pg.112]

Fig. 4.3. The dispersion of polariton in cubic crystals. Nongyrotropic crystals (a) The dependences of exciton and photon energy on wavevector, the retardation neglected (b) the same but with retardation taken into account. The symbols and L indicate longitudinal and transverse polarization of excitons (c) retardation neglected but dependence of the exciton energy on the wavevector taken into account here and in (d), (e), and (f) only the lower branch of the polaritons shown (d) the retardation and dependence of exciton energy on wavevector are taken into account. Gyrotropic crystals (e) Dispersion of excitons in the cubic gyrotropic crystals if retardation is neglected (f) the same when retardation is also taken into account Aq denotes the position of the bottom of the polariton energy. Fig. 4.3. The dispersion of polariton in cubic crystals. Nongyrotropic crystals (a) The dependences of exciton and photon energy on wavevector, the retardation neglected (b) the same but with retardation taken into account. The symbols and L indicate longitudinal and transverse polarization of excitons (c) retardation neglected but dependence of the exciton energy on the wavevector taken into account here and in (d), (e), and (f) only the lower branch of the polaritons shown (d) the retardation and dependence of exciton energy on wavevector are taken into account. Gyrotropic crystals (e) Dispersion of excitons in the cubic gyrotropic crystals if retardation is neglected (f) the same when retardation is also taken into account Aq denotes the position of the bottom of the polariton energy.
Before discussing this new method it is useful to recall briefly the methods which we have already discussed. Note, first of all that calculations of the dielectric tensor must be based, as is known, upon a microscopic theory Such a theory for ionic crystals was first developed by Born and Ewald (2) for the infrared spectral region. The application of this approach for the region of exciton resonances has also been demonstrated in (3). In an approach identical to that of Born and Ewald (2) the mechanical excitons (see Section 2.2) are taken as states of zeroth-approximation. In the calculation of these states the Coulomb interaction between charges has to be taken into consideration without the contribution of the long-range macroscopic part of the longitudinal electric field. If this procedure can be carried out, then the Maxwell total macroscopic fields E and H can be taken as perturbations. In the first order of perturbation theory, we find... [Pg.215]

The main difficulty, which may arise by applying the above-described scheme with mechanical excitons, consists in the necessity of excluding the macroscopic longitudinal electrical field from the equations of motion (or from the Coulomb Hamiltonian) in the calculation of the unperturbed zeroth-approximation states. [Pg.215]

For ionic crystals, within the classical treatment of ion motion (see (2)), and for molecular crystals in the Frenkel exciton spectral region (see (3) and Section 2.2), the Ewald procedure was successfully used to exclude the macroscopic part of longitudinal field. This permitted one to compute the tensor e j(w, k) using the... [Pg.215]

The values a(w,k) and b(v, k) have resonances at frequencies corresponding to longitudinal and transverse polaritons. If one takes into account the dissipation, the imaginary parts of the polariton energies would appear in the denominators of these expressions. As longitudinal excitons do not interact with the transverse electric field, the resonances of a(v, k) coincide with the frequencies of longitudinal Coulomb excitons. [Pg.223]

For electronic transitions in a dielectric the frequencies of Coulomb surface excitons are in the region of the longitudinal-transverse splitting, which is always small in comparison with the frequencies uy. Taking this fact into account, eqn (12.80) can be changed into... [Pg.357]

Since the excited states are electrically neutral, only the short-range, acoustic interaction is relevant in eqn (7.24). (This is also true for the exciton-polaron, as the particle and hole are closely separated.) The polaron, however, being charged also couples to the longitudinal optic phonons, so the long-range term is retained... [Pg.111]


See other pages where Exciton longitudinal is mentioned: [Pg.881]    [Pg.881]    [Pg.300]    [Pg.36]    [Pg.44]    [Pg.71]    [Pg.60]    [Pg.52]    [Pg.71]    [Pg.540]    [Pg.171]    [Pg.444]    [Pg.90]    [Pg.163]    [Pg.112]    [Pg.121]    [Pg.224]    [Pg.235]    [Pg.266]    [Pg.272]    [Pg.331]    [Pg.331]    [Pg.331]    [Pg.376]    [Pg.447]    [Pg.173]    [Pg.323]    [Pg.324]    [Pg.521]    [Pg.540]    [Pg.280]    [Pg.107]    [Pg.572]    [Pg.572]   
See also in sourсe #XX -- [ Pg.235 , Pg.331 ]




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